Expand the following:(3a - 2b)^3 | vedclass

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(A) To expand the expression $(3a - 2b)^3$,we use the algebraic identity:$(x - y)^3 = x^3 - y^3 - 3xy(x - y)$Here,$x = 3a$ and $y = 2b$.Substituting t

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$27a^3 - 8b^3 - 54a^2b + 36ab^2$

Vedclass · Answer

(A) To expand the expression $(3a - 2b)^3$,we use the algebraic identity:$(x - y)^3 = x^3 - y^3 - 3xy(x - y)$Here,$x = 3a$ and $y = 2b$.Substituting these values into the identity:$(3a - 2b)^3 = (3a)^3 - (2b)^3 - 3(3a)(2b)(3a - 2b)$Calculate the cubes:$(3a)^3 = 27a^3$$(2b)^3 = 8b^3$Now,simplify the expression:$= 27a^3 - 8b^3 - 18ab(3a - 2b)$Distribute $-18ab$ into the parentheses:$= 27a^3 - 8b^3 - (18ab 	imes 3a) + (18ab 	imes 2b)$$= 27a^3 - 8b^3 - 54a^2b + 36ab^2$

Expand the following:
$(3a - 2b)^3$

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Expand the following:$(3a - 2b)^3$